Cucker-Smale flocking particles with multiplicative noises: stochastic mean-field limit and phase transition
Abstract
In this paper, we consider the Cucker-Smale flocking particles which are subject to the same velocity-dependent noise, which exhibits a phase change phenomenon occurs bringing the system from a "non flocking" to a "flocking" state as the strength of noises decreases. We rigorously show the stochastic mean-field limit from the many-particle Cucker-Smale system with multiplicative noises to the Vlasov-type stochastic partial differential equation as the number of particles goes to infinity. More precisely, we provide a quantitative error estimate between solutions to the stochastic particle system and measure-valued solutions to the expected limiting stochastic partial differential equation by using the Wasserstein distance. For the limiting equation, we construct global-in-time measure-valued solutions and study the stability and large-time behavior showing the convergence of velocities to their mean exponentially fast almost surely.
Keywords
Cite
@article{arxiv.1711.10371,
title = {Cucker-Smale flocking particles with multiplicative noises: stochastic mean-field limit and phase transition},
author = {Young-Pil Choi and Samir Salem},
journal= {arXiv preprint arXiv:1711.10371},
year = {2017}
}